An Historical Outline of the Calculus
Some Problems Motivating the Development of the Calculus
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determination of instantaneous velocity and acceleration
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find the line tangent to a curve -- optics
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determining the maximum (or minimum) value of a function -- canon fire
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determining the length of a curve, the area bounded by a curve, or volumes
of certain solids -- used in the study of planetary orbits
Some Contributors to Integration Theory
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Archimedes (3rd Century B.C.) -- computed area using Eudoxus' method
of exhaustion
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Simon Stevin (16th Century A.D.) -- Flemish engineer who computed
force on a dam due to fluid pressure using methods related to Archimedes'
techniques
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Johann Kepler (16th Century A.D.) -- needed to compute area in applying
his Second Law of Planetary Motion
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Bonaventura Cavalieri (17th Century A.D.) -- used his theory of
indivisibles for various area and volume calculations
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John Wallis (17th Century A.D.) -- systematized the works of Cavalieri
Some Contributors to Differentiation Theory
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Pierre Fermat (17th Century) -- used Kepler's ideas to determine
minima and maxima of functions, devised procedure for determining tangent
lines
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Isaac Barrow (17th Century) -- further work on determining tangent
lines, recognized the Fundamental Theorem of Integral Calculus, teacher
of Isaac Newton
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Willhelm Leibniz and Isaac Newton (17th Century) -- devised
a symbolism and system of rules for computing derivatives and integrals
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Augustin-Louis Cauchy (19th Century) -- began the establishment
of a rigorous foundation for the calculus of Leibniz and Newton
References
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An Introduction to the History of Mathematics, by Howard Eves
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Calculus, by Stanley Grossman